In a small bowl, beat together the cream cheese, basil, chives and garlic with an electric mixer until smooth; set aside. Slice each tomato into 4 thick slices, discarding ends. Place tomato slices in a single layer in a large grill basket.
For a charcoal grill, place grill basket on the rack of an uncovered grill directly over medium-hot coals. Grill tomatoes 6 to 8 minutes or until just tender and starting to brown on edges, turning once. (For a gas grill, preheat grill. Reduce heat to medium-hot. Place grill basket on grill rack over heat. Cover and grill as above.)
To serve, spread bottoms of each roll with the herbed cream cheese mixture. Place 2 tomato slices on each roll. Add roll tops. Makes 4 sandwiches.
For a lower-fat version, substitute reduced-fat cream cheese for the regular cream cheese.